Data-driven reconstruction of band dispersion and quantum geometry via Koopman dynamical mode decomposition
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913100869926912 |
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| author | Pan, Yiming He, Jinze Yang, Jiapeng Fan, Zhiwei |
| author_facet | Pan, Yiming He, Jinze Yang, Jiapeng Fan, Zhiwei |
| contents | We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band dispersion and modal dynamics directly from spatiotemporal data, including wavefunctions and observables. This framework establishes a correspondence between Hamiltonian Floquet-Bloch decomposition and Koopman-DMD, whereby the extracted DMD modes encode frequencies, decay or growth rates, spatial profiles and projection weights. These quantities allow the reconstruction of spectral functions, local density of states, and delocalized-to-localized measures such as the inverse participation ratio. Also, these extended DMD modes enable inference of quantum-geometric and topological properties, including the quantum metric, Berry curvature and geometric phases. Applications to prototypical one- and two-dimensional tight-binding models, including disordered Su-Schrieffer-Heeger model and its Floquet and non-Hermitian variants, graphene and Haldane models, demonstrate that Koopman-DMD provides a unified route for the data-driven analysis of wave propagation, localization, and topological phases in condensed matter, photonics, and related fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-driven reconstruction of band dispersion and quantum geometry via Koopman dynamical mode decomposition Pan, Yiming He, Jinze Yang, Jiapeng Fan, Zhiwei Computational Physics We present a data-driven framework for reconstructing band structures using Koopman operator analysis and dynamic mode decomposition (Koopman-DMD). Instead of deriving spectra from an explicit Hamiltonian, the approach reconstructs band dispersion and modal dynamics directly from spatiotemporal data, including wavefunctions and observables. This framework establishes a correspondence between Hamiltonian Floquet-Bloch decomposition and Koopman-DMD, whereby the extracted DMD modes encode frequencies, decay or growth rates, spatial profiles and projection weights. These quantities allow the reconstruction of spectral functions, local density of states, and delocalized-to-localized measures such as the inverse participation ratio. Also, these extended DMD modes enable inference of quantum-geometric and topological properties, including the quantum metric, Berry curvature and geometric phases. Applications to prototypical one- and two-dimensional tight-binding models, including disordered Su-Schrieffer-Heeger model and its Floquet and non-Hermitian variants, graphene and Haldane models, demonstrate that Koopman-DMD provides a unified route for the data-driven analysis of wave propagation, localization, and topological phases in condensed matter, photonics, and related fields. |
| title | Data-driven reconstruction of band dispersion and quantum geometry via Koopman dynamical mode decomposition |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2605.06199 |